Open the case and make sure no lights or anything come on when you hit the switch. Also, make sure the PSU fan doesn't start up. It could also be the switch that tells the PSU to turn on, but it's most likely the power supply. You can short two wires on the PSU if you really want to make sure it isn't the case switch. You can Google which wires, but I would suggest checking the forums on the PSU manufacturers website. I've heard of a few generic PSUs that don't like being shorted, but that's more the exception than the rule.

Chech the power switch on the back of the power supply too. sometimes that gets hit. It could also be a bad power cable, bad surge protector, or bad outlet. Individual power ports on a surge protector have been known to go bad.

Raolan is on the correct path to check the internals. if you have anything internal spinning up or blinkiing, you have power.

Yeah, I couldn't hear anything when I tried powering it up, but I'll give it a visual since I have to open it up anyways. In regards to cable and such, this older computer that I'm using as a substitute powered up just fine on it, so that's a plus.

If you don't go with a Corsair model, make sure you are getting an 80+ certified model (some descriptions may not mention 80+, but may mention being certified for nVidia SLI). Otherwise, eventually your PSU may only be able to deliver output in the 60-70% range under sustained loads, so you'll need to pad the rating a bit (basically, go a tier higher: instead of a generic 600w, go with 700/750w, etc.).

I know the prices may look a bit steep for the 80+ models, but these new GPU's combined with the multi-core CPU's can really hammer a PSU--and when those generic models get hot, their output drops off pretty quick. You may actually save money in the long run with a higher quality PSU because of the longer warranties. I got a Corsair TX650 on sale a while back at Best Buy for $85--and it has a 5yr warranty (Corsair typically just swaps things out, so their warranties usually translate to free replacement). Even their entry level CX models have 2 years--Pro lines have 7.